Simplify; express your answer in exponential form. Assume $n\neq 0, p\neq 0$. $\dfrac{{n^{-2}}}{{(n^{-1}p^{5})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${n^{-2}}$ to the exponent ${1}$ . Now ${-2 \times 1 = -2}$ , so ${n^{-2} = n^{-2}}$ In the denominator, we can use the distributive property of exponents. ${(n^{-1}p^{5})^{2} = (n^{-1})^{2}(p^{5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{n^{-2}}}{{(n^{-1}p^{5})^{2}}} = \dfrac{{n^{-2}}}{{n^{-2}p^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{-2}}}{{n^{-2}p^{10}}} = \dfrac{{n^{-2}}}{{n^{-2}}} \cdot \dfrac{{1}}{{p^{10}}} = n^{{-2} - {(-2)}} \cdot p^{- {10}} = p^{-10}$.